Diffusion on fractal lattices and the fractal Einstein relation

Abstract

Finitely ramified fractal lattices show anomalous diffusion with (r 2) varies as t2H. There is a hierarchy of transit times which are shown by Monte Carlo simulation to satisfy ( tau n) varies as alpha n for large n, where alpha =b1H/ and b is the base of the lattice. The lattice resistivity scales with size as rho varies as Rn where R is characteristic of the lattice. Exact renormalisation group methods yield alpha and R analytically and verify the Einstein relation for fractals alpha =RN.